This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A170946 #51 Feb 12 2025 07:52:18 %S A170946 1,2,5,20,107,870,9436,122840,1863359,32019826,613981447,12989756316, %T A170946 300559406027,7550660328494,204687564072918,5955893472990664, %U A170946 185158932576089787,6125200100394894738,214837724735760642773,7963817561236130021156,311101285883236139915989 %N A170946 Number of sensed unrooted combinatorial maps with n edges. %C A170946 Also number of "dessins d'enfants" with n edges. - _Mark van Hoeij_, Jan 23 2011 %C A170946 a(n) also counts the Feynman diagrams of the QED vacuum polarization with 2*n vertices: fermion lines (resp. boson lines, vertices) of the Feynman diagrams correspond to the vertices (resp. edges, darts) of the combinatorial maps, and the circular order of the edges around each vertex in a map is encoded in the topology of the corresponding Feynman diagram. - _Andrey Zabolotskiy_, Jan 28 2025 %H A170946 Andrew Howroyd, <a href="/A170946/b170946.txt">Table of n, a(n) for n = 0..400</a> (terms 1..30 from Antonio Breda d'Azevedo, Alexander Mednykh and Roman Nedela) %H A170946 Antonio Breda d'Azevedo, Alexander Mednykh and Roman Nedela, <a href="https://doi.org/10.1016/j.disc.2009.11.017">Enumeration of maps regardless of genus: Geometric approach</a>, Discrete Mathematics, Volume 310, 2010, Pages 1184-1203. %H A170946 N. M. Adrianov, N. Ya. Amburg, V. A. Dremov, Yu. A. Levitskaya, E. M. Kreines, Yu. Yu. Kochetkov, V. F. Nasretdinova and G. B. Shabat, <a href="http://arxiv.org/abs/0710.2658">Catalog of dessins d'enfants with <= 4 edges</a>, arXiv:0710.2658 [math.AG], 2007. %H A170946 R. J. Mathar, <a href="http://vixra.org/abs/1901.0148">Feynman diagrams of the QED vacuum polarization</a>, vixra:1901.0148 (2019), Section V. Computed up to a(5), plotted up to a(4). %H A170946 R. de Mello Koch and S. Ramgoolam, <a href="https://doi.org/10.1103/PhysRevD.85.026007">Strings from Feynman graph counting: without large N</a>, Phys Rev D, 85 (2012) 026007; arXiv:<a href="https://arxiv.org/abs/1110.4858">1110.4858</a> [hep-th], 2011-2012. The terms in Eq. (D.10) from a(7) on are erroneous. %Y A170946 Row sums of A379438 and A380615. %Y A170946 Cf. A170947 (achiral), A214816 (unsensed). %Y A170946 Cf. A268558 (inv. Euler Transf.) %K A170946 nonn %O A170946 0,2 %A A170946 _N. J. A. Sloane_, Feb 21 2010 %E A170946 a(0)=1 prepended by _Andrew Howroyd_, Jan 28 2025